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第三十二届中国控制会议

作者： LI Xin SONG Kaoping SUN Ning ZHAO Chunli School of Computer & Information Technology Northeast Petroleum University School of Petroleum Engineering Northeast Petroleum University

ISBN: (纸本)9781479900305

When the grover's algorithm is applied to search an unordered database, the probability of getting correct results usually decreases with the increase of marked items. The reason for this phenomenon is analyzed in this Letter, the grover iteration is studied, and a new phase matching is proposed. With application of the new phase matching, when the fraction of marked items is greater than 1/3, the probability of getting correct results is greater than 25/27 with only one grover iteration. The validity of the new phase matching is verified by a search example.

关键词： Quantum computing Quantum searching grover algorithm Phase matching

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Quantum Cryptography based on grover's algorithm

Quantum Cryptography based on Grover's Algorithm

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2nd International Conference on Innovative Computing Technology (INTECH)

作者： Sakhi, Z. Tragha, A. Kabil, R. Bennai, M. Hassan II Mohamedia Univ Lab Informat Technol & Modelisat Ben Msik Fac Sci Casablanca Morocco

ISBN: (纸本)9781467326797

Some cryptographic applications of quantum algorithm on many qubits system are presented. We analyze a basic concept of grover algorithm and it's implementation in the case of four qubits system. We show specially that grover algorithm allows as obtaining a maximal probability to get the result. Some features of quantum cryptography and Quantum Secret-Sharing protocol based on grover's algorithm are also presented.

关键词： Qubit quantum cryptography grover algorithm

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Multi-pattern recognition based on grover's algorithm

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CHINESE JOURNAL OF ELECTRONICS 2007年第4期16卷 679-682页

作者： Zhou Rigui Jiang Nan Ding Qiulin Nanjing Univ Aeronaut & Astronaut Dept Comp Sci & Technol Nanjing 210016 Peoples R China

In recent years there has been an increasing focus on the pattern recognition, especially multi-pattern recognition in computer science. This paper investigates the issue in a new way built upon the quantum computation theory and presents a multi-pattern recognition method based on grover's algorithm. This method not only introduces a new design scheme of initializing quantum state and quantum encoding on the pattern set, but also details the process of quantum multi-pattern recognition using several unitary operators. Owing to the power of quantum parallelism, this new method can recognize multi-pattern simultaneously with a certain probability in the given pattern set. Mathematic calculations and simulation result in recognizing "XOR" and three-class hybrid pattern show that the proposed method can accomplish multi-pattern recognition with the probability of almost 80%, which displays one tempting foreground for quantum multi-pattern recognition.

关键词： multi-pattern recognition grover algorithm initializing quantum state three-class hybrid pattern

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grover quantum searching algorithm based on weighted targets

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Journal of Systems Engineering and Electronics 2008年第2期19卷 363-369页

作者： Li Panchi Li Shiyong Dept. of Control Science and Engineering Harbin Inst. of Technology Harbin 150001 P. R. China Dept. of Computer Science and Engineering Daqing Petroleum Inst. Daqing 163318 P. R. China

The current grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal. To solve this problem, a grover searching algorithm based on weighted targets is proposed. First, each target is endowed a weight coefficient according to its importance. Applying these different weight coefficients, the targets are represented as quantum superposition states. Second, the novel grover searching algorithm based on the quantum superposition of the weighted targets is constructed. Using this algorithm, the probability of getting each target can be approximated to the corresponding weight coefficient, which shows the flexibility of this algorithm. Finally, the validity of the algorithm is proved by a simple searching example.

关键词： grover algorithm targets weighting quantum searching quantum computing.

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Speedup of grover's search algorithm and closed timelike curves

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QUANTUM SCIENCE AND TECHNOLOGY 2020年第4期5卷

作者： Yee, Ki Hyuk Bang, Jeongho Alsing, Paul M. Miller, Warner A. Ahn, Doyeol Univ Seoul Dept Elect & Comp Engn 163 Seoulsiripdae Ro Seoul 02504 South Korea Korea Inst Adv Study Sch Computat Sci Seoul 02455 South Korea Informat Directorate Air Force Res Lab Rome NY 13441 USA Florida Atlantic Univ Phys Dept Boca Raton FL 33431 USA Peta Lux Inc 12 Yanghyeon Ro 405 Beon Gill Seongnam 13438 Gyeonggi Do South Korea

The quadratic reduction of query complexity of grover's search algorithm (GA), while significant, would not be enough to enjoy exponentially fast data searching in large-scale quantum computation. One of the ways to enhance the speedup in the framework of grover's algorithm is to employ a novel quantum operation, i.e., inversion against an unknown state;however, this is not possible at least in quantum theory. We thus extend the grover algorithm assisted by closed timelike curves (CTCs), in which the unknown-state inversion is achievable by combining the superposition of two unknown states with cloning. We dubbed this refined algorithm CTC-assisted grover algorithm (CTC-GA). We show that the CTC-GA can vastly reduce the query complexity compared to the original algorithm;remarkably, from polynomial to poly-logarithmic. These results will provide a broader intuition for exponential quantum speedup of data searching problems.

关键词： grover algorithm closed timelike curve quantum algorithm search speedup

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Circuit optimization of grover quantum search algorithm

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QUANTUM INFORMATION PROCESSING 2023年第1期22卷 1-11页

作者： Wu, Xi Li, Qingyi Li, Zhiqiang Yang, Donghan Yang, Hui Pan, Wenjie Perkowski, Marek Song, Xiaoyu Yangzhou Univ Coll Informat Engn Yangzhou 225000 Peoples R China Cent South Univ Business Sch Changsha 410083 Peoples R China Portland State Univ Dept ECE Portland OR 97207 USA

grover algorithm is a quantum search algorithm that can find the target state efficiently. However, with the increase in the amount of searching data, the circuit of grover algorithm is faced with complex gate decomposition problem. In today's NISQ era, resources are very limited, so the depth of circuit is an important metric. This paper introduces a two-stage quantum search algorithm based on divide-and-conquer, which can run quickly in parallel on a quantum computer. A circuit optimization method is proposed to reduce the number of iterations by using block-level oracle circuit. Combining this method with divide-and-conquer idea, it is defined as the 2P-grover algorithm. The simulation experiment was carried out on the quantum computing framework Cirq and compared with grover algorithm. The experimental results show that the 2P-grover algorithm can reduce the depth of circuit by at least 1.2 times and maintain a high probability of search success.

关键词： Quantum circuit grover algorithm QPSA algorithm Quantum information Cirq framework

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Quantum search with certainty based on modified grover algorithms: optimum choice of parameters

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QUANTUM INFORMATION PROCESSING 2013年第5期12卷 1897-1914页

作者： Toyama, F. M. van Dijk, W. Nogami, Y. Kyoto Sangyo Univ Dept Comp Sci Kyoto 6038055 Japan Redeemer Univ Coll Dept Phys Ancaster ON L9K 1J4 Canada McMaster Univ Dept Phys & Astron Hamilton ON L8S 4M1 Canada

In the original grover algorithm, an exact or almost exact search such that the success probability is unity or infinitesimally close to unity is possible only for certain values of the fraction lambda = M/N where M is the number of marked items that are stored in an unsorted database of N items. There are various modified algorithms with an adjustable phase or phases such that an exact search can be done for any value of lambda by means of a finite number of grover-type operations. Among them, the algorithm proposed by Long is the simplest in the sense that it has only one adjustable phase and that the phase can be obtained in a closed form. We show that other more general algorithms with additional phases are not more efficient than Long's version with a single phase.

关键词： Quantum computing Quantum search grover algorithm Phase matching

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Zero-correlation linear analysis for block ciphers based on the Bernstein-Vazirani and grover algorithms

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QUANTUM INFORMATION PROCESSING 2024年第8期23卷 289-289页

作者： Zhang, Kun Shang, Tao Tang, Yao Liu, Jianwei Beihang Univ Sch Cyber Sci & Technol Beijing 100083 Peoples R China

With the rapid development of quantum computing technology, the traditional cryptosystem will face a significant threat. It is an urgent security issue to study the security impact of quantum computing on classical cryptosystems and provide reliable cryptographic primitives for the post-quantum era. A powerful way to solve this problem is to quantize the classical cryptanalysis tools and use the improved versions for cryptanalysis. In this paper, we propose a quantum Zero-correlation analysis algorithm based on the Bernstein-Vazirani and grover algorithms. It can find zero-correlation linear hulls for Feistel and SPN structures. We prove the correctness of the algorithm and analyze its complexity. Compared with the classical algorithms, the proposed quantum algorithm has significant advantages when the number of encryption rounds of block ciphers is large. Moreover, compared with the existing quantum Zero-correlation linear analysis, the proposed algorithm is more efficient and does not depend on the algebraic characteristics of the target cipher, which makes the algorithm has more flexible application scenarios. With the development of quantum computers, we discuss the threat of quantum cryptanalysis algorithms to classical security.

关键词： Quantum cryptography Quantum computing Block cipher Bernstein-Vazirani algorithm grover algorithm

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A grover based Quantum algorithm for Finding Pure Nash Equilibria in Graphical Games 19

A Grover based Quantum Algorithm for Finding Pure Nash Equil...

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19th IEEE International Conference on Software Architecture (ICSA)

作者： Roch, Christoph Castillo, Santiago Londotio Linnhoff-Popien, Claudia Ludwig Maximilians Univ Munchen Inst Comp Sci Munich Germany

ISBN: (纸本)9781665494939

The grover algorithm and its underlying amplitude amplification process are one of the most essential and widely used building blocks of many other subsequent quantum methods. In this work, we adapt grover's search algorithm to find pure Nash equilibria in graphical games. In general, the main complexity lies in the construction of the algorithm's oracle operator. We show how to set up the oracle from a given graphical game by translating it to a Boolean satisfiability problem, which can subsequently be logically synthesized to an oracle quantum circuit. We investigate the algorithm for random graphical game instances on IBM's quantum simulator and give an outlook regarding the scaling of it.

关键词： grover algorithm Quantum Nash Equilibrium Graphical Game Boolean Satisfiability Problem

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A solution to implement grover quantum computation algorithm using the binary representation of the phase on the FPGA 11

A solution to implement Grover quantum computation algorithm...

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11th International Conference on Electronics, Computers and Artificial Intelligence (ECAI)

作者： Ionescu, Laurentiu-Mihai Mazare, Alin Gheorghita Serban, Gheorghe Ioan, Lita Visan, Daniel Univ Pitesti Dept Elect Comp & Elect Engn Pitesti Romania

ISBN: (纸本)9781728116242

The system proposed in this paper will be used to implement the Groove quantum computation search algorithm: look in a content addressable memory and find location for a data. Unlike other solutions implemented in FPGA, our solution is trying to achieve the performance of a quantum computing system on resources allocated and search speed.

关键词： Quantum computing FPGA grover algorithm

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